Page 81 - Applied Statistics with R

5.3. SIMULATION 81

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→ ( , 2 ) .

The following verifies this result for a Poisson distribution with = 10 and a
sample size of = 50.

set.seed(1337)
mu = 10
sample_size = 50
samples = 100000
x_bars = rep(0, samples)

for(i in 1:samples){
x_bars[i] = mean(rpois(sample_size, lambda = mu))
}

x_bar_hist = hist(x_bars, breaks = 50,
main = "Histogram of Sample Means",
xlab = "Sample Means")

Histogram of Sample Means

8000

Frequency 6000 4000

2000

0
8 9 10 11 12

Sample Means

Now we will compare sample statistics from the empirical distribution with their
known values based on the parent distribution.